2x^2+10x-96.5=0

Solution for 2x^2+10x-96.5=0 equation:

2x^2+10x-96.5=0

a = 2; b = 10; c = -96.5;
Δ = b2-4ac
Δ = 102-4·2·(-96.5)
Δ = 872
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{872}=\sqrt{4*218}=\sqrt{4}*\sqrt{218}=2\sqrt{218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{218}}{2*2}=\frac{-10-2\sqrt{218}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{218}}{2*2}=\frac{-10+2\sqrt{218}}{4}
$